Math

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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=9-x^2. What are the dimensions of such a rectangle with the greatest possible area?

  • Math -

    let the point of contact in the first quadrant be (x,y)
    then the base of the rectangle is 2x and its height is y
    Area = 2xy
    = 2x(9-x^2)
    = 18x - 2x^2
    d(area)/dx = 18 - 4x
    so 18-4x=0
    x = ....

    take it from here, let me know what you got

  • oops Math -

    change
    << = 18x - 2x^2 >> to

    = 18x - 2x^3

    then d(area)/dx = 18 - 6x^2
    = 0 for a max/min of area
    6x^2 = 18
    x^2 = 3
    x = ±√3
    and y = 6

    same result as Damon

  • Math -

    Well, this is an upside down parabola (sheds water) with x intercepts at x = -3 and x = +3 and vertex at (0,9)
    so lets do it just for positive x and double the base at the end.
    Area = x y
    where y = 9-x^2
    A = 9x - x^3
    dA/dx = 9 - 3 x^2
    that is zero when x^2 = 3
    or x = +/- sqrt 3 use + sqrt 3
    so y = 9 - 3 = 6
    Now we double the base because we only did the right half
    base = 2 sqrt 3
    height = 6

  • Math -

    how do I write a written equation? A jacket cots 28.00 more than twice the cost of a pair of slacks. If the jacket costs 152.00, how much do th slacks cost?

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